Poincaré series for GL(n): Fourier expansion, Kloosterman sums, and algebreo-geometric estimates

DOI10.1007/BF01163653zbMath0612.10020MaRDI QIDQ1087903

Solomon Friedberg

Publication date: 1987

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173873

zbMATH Keywords

Weyl groupexponential sumscharacter sumsKloosterman sumFourier expansionsGL(n) Poincaré series

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Estimates on character sums (11L40) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (19)

Mellin transforms of Whittaker functions ⋮ Parametrization of Kloosterman sets and \(\mathrm{SL}_3\)-Kloosterman sums ⋮ Applications of the Kuznetsov formula on \(\mathrm{GL}(3)\). II: The level aspect ⋮ On sums of hyper-Kloosterman sums ⋮ Bessel functions and Kloosterman integrals on \(\mathrm{GL}(n)\) ⋮ Density theorems for \(\mathrm{GL}(n)\) ⋮ On sums of \(\mathrm{SL}(3,\mathbb{Z})\) Kloosterman sums ⋮ Unnamed Item ⋮ Kloosterman sums for Clifford algebras and a lower bound for the positive eigenvalues of the Laplacian for congruence subgroups acting on hyperbolic spaces ⋮ The fundamental lemma of Jacquet and Ye in positive characteristic ⋮ Exponential sums and \(\ell\)-adic cohomology: A survey. ⋮ Evaluating Jacquet’s $\mathbf {{\rm GL}(n)}$ Whittaker function ⋮ The Spectral Kuznetsov Formula on $SL(3)$ ⋮ The Relative Trace Formula in Analytic Number Theory ⋮ Applications of analytic newvectors for \(\operatorname{GL}(N)\) ⋮ Kloosterman sets in reductive groups ⋮ Symplectic Kloosterman sums and Poincaré series ⋮ An orthogonality relation for (with an appendix by Bingrong Huang) ⋮ Germs of Kloosterman Integrals for $GL(3)$

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Automorphic forms on GL(3,\({\mathbb{R}})\)
• Poincaré series on \(\mathrm{GL}(r)\) and Kloosterman sums
• Theory of Eisenstein series for the group SL(3,R) and its application to a binary problem
• Kloosterman sums and Fourier coefficients of cusp forms
• The multiplicity one theorem for \(\mathrm{GL}_n\)
• Sums of Kloosterman sums
• Poincaré series and Kloosterman sums for SL(3, Z)
• On Some Exponential Sums

This page was built for publication: Poincaré series for GL(n): Fourier expansion, Kloosterman sums, and algebreo-geometric estimates